A simple evaluation of adiabatic proton tunneling across the electrified double layer

Coupled proton-electron transfer (CPET) reactions are likely to play a pivotal role in the global transition to a sustainable energy future. Our atomic scale understanding of this class of reactions has been significantly improved by developments in density functional theory (DFT) simulations. Here, the ultimate goal is to intelligently predict rates of CPET reactions at the electrified double layer to design new catalysts and maximize their real-world applications. These studies often utilize harmonic transition state theory (HTST), which, among other things, assumes that quantum tunneling through energy barriers is negligible. In this study, we present a simple evaluation of the contribution of quantum tunneling in adiabatic CPET reactions to evaluate this assumption. We investigate the effect of different potential profiles on tunneling probabilities and compare these profiles with calculated CPET minimum energy paths (MEPs). We find that the calculated CPET MEPs are significantly stiffer than the commonly used Eckart profile, and study the effect of changing barrier height and width on overall zero curvature tunneling correction factors. We find that, depending on the reaction of interest and the bulk pH, proton tunneling may not be a negligible phenomenon for CPET reactions at the electrified double layer. In particular, reactions involving large barriers and short distances are predicted to have significant contributions from non-classical tunneling, possibly explaining observed kinetic isotope effects for the hydrogen evolution reaction on Au in alkaline media. Our model choices are significantly simplified -- for example, neglecting the effects of reaction coordinate curvature and vibronic coupling -- suggesting that our predicted tunneling contributions may be significantly underestimated. However, our findings provide a simple way to evaluate whether tunneling is relevant for a particular CPET reaction of interest.